I. Introduction To The Invention
The invention herein is an outgrowth of research into the superconductive phenomenon by the Inventor since 1966, and particularly, his Master of Science Thesis of 1974 at the University of Detroit, entitled "A Thermodynamic Comparison between the Magento-Mechanically and Magneto-Calorically Induced Superconductive Phase Transitions in a Type I Superconductor Culminating in a Proposal for a New Type of Suprconductive Motor", which is hereby incorporated by reference. This thesis elucidated a cyclic process, and several embodiments, for a heat engine utilizing superconductors as the working substance. The present Invention is an entirely new approach, however, to the problem of achieving a successful closed thermodynamic cycle.
The essential drawback to any energies conversion process is the rejection of waste heat to the low temperature reservoir when above absolute zero. It is the subject of the Invention herein to fully describe a cyclic process for superconductors whereby heat may be directly converted into work, with no waste heats rejection to a low temperature region, independent of its temperature.
(a) Superconductivity, An Historical Summary PA1 (b) Summary PA1 (c) Advantages PA1 (d) Materials PA1 (e) Utility PA1 1. Diamagnetic Work as a reaction to field change, in either electrical or mechanical terms; PA1 2. Specific Heat as a result of temperature variation in either the superconductive or normal phases; PA1 3. Latent Heat as a result of phase variation wherein the phases have different entropy. PA1 (a) Steps to Achieve a Closed Cycle PA1 (1) Isothermal Magnetization: H.sub.1 to H.sub.2 @ T.sub.1 : (H.sub.1.sup.2 -H.sub.2.sup.2)/8.pi..multidot.V.sub..omega. (in) PA1 (2) Isomagnetic Cooling: T.sub.1 to T.sub.2 @ H.sub.2 : .intg.C.sub.n .multidot.dT.multidot.V+LH.sub.2 .multidot.V (out) PA1 (3) Isothermal Demagnetization: H.sub.2 to H.sub.1 @ T.sub.2 : (H.sub.2.sup.2 -H.sub.1.sup.2)/8.pi..multidot.(V+V.sub..omega.) (out) PA1 (4) Isomagnetic Heating: T.sub.2 to T.sub.1 @ H.sub.1 : .intg.C.sub.s .multidot.dT.multidot.V+LH.sub.1 .multidot.V (in), where V is the specimen volume and V.sub..omega. is the volume of the magnetic working space enclosing the specimen. PA1 1. Analysis of Useful Works PA1 2. Analysis of Heat Fuel PA1 3. Analysis of Step Paths PA1 (b) Operative Considerations PA1 (c) Cyclical Considerations PA1 (d) Embodiment Considerations PA1 (A) General PA1 (B) Macroscopic Description PA1 (C) The Magneto-Caloric Effect PA1 (D) Microscopic Description: Primary Formulation PA1 (F) Microscopic Description: Secondary Formulation PA1 (G) Application of the Description of the Magneto-Caloric Effect PA1 (H) Means to Predict the Instantaneous Entropy Value During Phase Transition PA1 1. Isothermal Adiabatic Magnetization: Phase varies from superconductive to normal, first evidenced by a change in magnetization of the segment to non-magnetic, with latent heat of cooling of T.sub.1 evidencing, via application of H=h.sub.1 +dH at T.sub.1. H is increased to H.sub.2 as defined by Step 2. Work done to increase the magnetic field in the case of a generator is (H.sub.2.sup.2 -H.sub.1.sup.2)/8.pi..multidot.V.sub..omega.', where V.sub..omega. is the volume occupied by the field (with .mu.=.mu..sub.o). There is no work necessary to move a normal Segment from H.sub.1 to H.sub.2 in the case of the motor embodiment. .DELTA.H/.DELTA.t is faster than .DELTA.T/.DELTA.t in Step 2, per the Tuyn Curve, so that always normal phase obtains. PA1 2. Isomagnetic Adiabatic Cooling: The latent heat of T.sub.1, LH.sub.1, causes the Segment to cool as the volume heat capacity supplies the difference in phase entropy energy at T.sub.1. The final low temperature attained, T.sub.2, is defined by: ##EQU28## where T.sub.2 satisfies the integral. 3. Isothermal Adiabatic Demagnetization: At T.sub.2, phase is caused to vary from normal to superconductive, which is a first evidenced by a change in magnetization of the segment to diamagnetic, by reducing the field from H.sub.2 to H.sub.2 -dH. H is decreased to H.sub.3, defined by T.sub.3 in Step 4. Energy removed from the field in its reduction in the case of a generator is: (H.sub.2.sup.2 -H.sub.3.sup.2)/8.pi..multidot.(V.sub..omega. +V.sub.s), where V.sub.s is the volume of the superconductive Segment. Work, in the case of a motor, is due to removal of the superconductive diamagnet from higher to lower field: (H.sub.2.sup.2 -H.sub.3.sup.2)8.pi..multidot.V.sub.s. The rate of change of H is such as to maintain the superconductive phase, per Step 4, i.e., H&lt;1-(T/T.sub.c).sup.2, where T.sub.c is the reduced critical temperature. PA1 4. Isomagnetic Adiabatic Heating: The latent heat of heating T.sub.2, LH.sub.2, will evolve upon phase variation in Step 3, where T.sub.2 &lt;0K. This difference in entropies of phase energy will be absorbed by the superconductive heat capacity, establishing a final higher temperature, T.sub.3, as: ##EQU29## where T.sub.3 satisfies the integral. 5. Isothermal Demagnetization: H, now at H.sub.3, is decreased to H.sub.1 by reducing the applied magnetic field in the case of a generator, or movement to lower magnetic field in the case of a motor. In the former, energy out is: (H.sub.3.sup.2 -H.sub.1.sup.2)/8.pi..multidot.(V.sub..omega. +V.sub.s), whereas in the latter, energy out is: (H.sub.3.sup.2 -H.sub.1.sup.2)/8.pi..multidot.V.sub.s. Variation in the magnetic field is at a rate so as to retain the superconductive phase, per Step 6. PA1 6. Isomagnetic Heating: The superconductive Segment is subjected to heat flow from a higher temperature region or reservoir until T.sub.1 is attained. The amount of heat energy, Q, is defined by: ##EQU30## Upon completion of heating, adiabatics is returned, and all initial conditions obtain PA1 Summary: PA1 1. Isothermal Adiabatic Demagnetization: Phase varies from normal to superconductive, first evidenced by a change in magnetization of the segment to diamagnetic, with a latent heat of heating to T.sub.1 resulting, via application of H=H.sub.1 -dH at T.sub.1. H is decreased to H.sub.2, which is defined by T.sub.2 in Step 2. Energy removed from the field in the case of a generator is: (H.sub.1.sup.2 -H.sub.2.sup.2)/8.pi..multidot.(V.sub..omega. +V.sub.s). In the case of a motor work is adduced via movement of the superconductive diamagnet from H.sub.1 to H.sub.2 as: (H.sub.1.sup.2 -H.sub.2.sup.2)/8.pi..multidot.V.sub.s. The rate of change of field is such as to always maintain the superconductive phase, per temperature variation in Step 2. PA1 2. Isomagnetic Adiabatic Heating: The latent heat of T.sub.1, LH.sub.1, causes the Segment to heat as the volume heat capacity absorbs the difference in phase entropy energy at T.sub.1. The final high temperature attained, T.sub.2, is defined by: ##EQU33## where T.sub.2 satisfies the integral. 3. Isothermal Adiabatic Magnetization: At T.sub.2, phase is caused to vary from superconductive to normal, which is first evidenced by a change in magnetization of the segment to non-magnetic, by increasing H so that H=H.sub.2 +dH. H is increased to H.sub.3, defined by T.sub.3 in Step 4. Energy added to the field due to increase in intensity, in the case of a generator is: (H.sub.3.sup.2 -H.sub.2.sup.2)/8.pi..multidot.V.sub..omega.. In the case of a motor, the absence of diamagnetism in the superconductor admits no work involvement in the relative motion to higher field. The rate of change of field is such as to retain the normal phase, while temperature changes due to Step 4. PA1 4. Isomagnetic Adiabatic Cooling: The latent heat of cooling of T.sub.2, LH.sub.2, will evolve upon phase variation in Step 3, where T.sub.2 &lt;T.sub.c. This difference in entropies of phase energy will be supplied by the volume normal heat capacity, adducing a final low temperature of T.sub.3, as: ##EQU34## where T.sub.3 satisfies the integral. 5. Isomagnetic Heating: The Segment is subjected to heat flow from a higher temperature region or reservoir until T.sub.1 is attained. The amount of energy, Q, is defined by: ##EQU35## 6. Isothermal Demagnetization: H, now at H.sub.3, is decreased to H.sub.1 by reducing the magnetic field in the case of a generator, or movement to lower field in the case of a motor embodiment. In the former, energy out is: (H.sub.3.sup.2 -H.sub.1.sup.2)/8.pi..multidot.V.sub..omega., whereas in the latter work is not involved in moving the non-magnetic Segment relative to a variable field value. The rate of change of field is such as to retain the normal phase, per the rate of change of temperature in Step 5. Upon completion of Demagnetization, adiabatics is returned, and all initial conditions obtain. PA1 Summary: PA1 1. Isothermal Demagnetization: Steps as in B.1, above. However, now H will decrease to H.sub.2 ', and the energies for the generator and motor will be respectively: (H.sub.1.sup.2 -H.sub.2 '.sup.2)/8.pi..multidot.(V.sub..omega. +V.sub.s) and (H.sub.1.sup.2 -H.sub.2 '.sup.2)/8.pi..multidot.V.sub.s. PA1 2. Isomagnetic Heating: In addition to LH.sub.1, Q' will enter, so that T.sub.2 ' is defined by: ##EQU41## 3. Isothermal Magnetization: Steps as in B.3, above. However, now, H will increase to only H.sub.1. This is because Q" will enter during Step 4, following, and admit only an increase of T to T.sub.1. Generator energy input will now be (H.sub.1.sup.2 -H.sub.2 '.sup.2)/8.pi..multidot.V.sub..omega.. Motor work will continue at zero, as the Segment is non-magnetic. PA1 4. Isomagnetic Cooling: In addition to LH.sub.2 ', which is the latent heat evolved at T.sub.2 ', of cooling, is the heat transfer of Q", which contributes a heating. The value of Q" is determined by: ##EQU42## With the attainment of T.sub.1, all the conditions at the start of the Cycle obtain. PA1 Summary:
H. Kamerlingh Onnes first successfully liquified helium by attaining 4.2.degree. K. in 1908. This achievement opened a new domain for scientific investigation: The unthinkably frigid zone just above the absolute zero of temperature. Onnes immediately recognized the vast potential his accomplishment created and decided to perform resistivity experiments at these heretofore unknown temperatures.
It was everyone's guess that electrical resistance would either cease, level off, or increase near absolute zero, either because of heat, impurity, or electronic condensation effects, respectively. Onnes decided to measure the resistive properties of mercury, to determine the nature of this electronic phenomenon, at liquid helium temperatures.
The resistance of mercury steadily declined with reduced temperature until suddenly at 4.152.degree. K., which was remarkably close to the helium boiling point, the metal lost all resistance to electric currents.
It was quickly speculated that this perfect or superconduction of electric current was due to some new condition within the sample yielding a state of infinite conductivity. Onnes and several other investigators performed tests with spheres of lead and other "superconductive" materials leading to the result that (A) conductivity was indeed perfect and (B) any incident magnetic field was excluded or not from the interior of such a lossless sample depending on its pre-history, that is, whether the field was applied before or after the material became superconducting.
It is not with little shock that the scientific community of 1933 was jolted by the news of an experiment by W. Meissner and R. Ochsenfeld which conclusively proved that the magnetic state of a superconductive sample is independent of its pre-history. Incredibly, the applied field which was present in their mono-crystal of tin above the transition temperature was summarily and completely expelled upon reducing the temperature below its critical value, T.sub.c. Therefore, the internal field is always zero while the metal is in the superconductive state.
How could such a wondrous mechanism, the so-called Meissner Effect, remain undetected for more than twenty years? (A) The previous experimenters had not been properly cautious and careful in taking readings on the fields outside their test samples. (B) Often hollow lead, etc., spheres were used in order to reduce helium refrigerant requirements, resulting in honestly mistaken measurements. (C) The theoreticians had created an entire body of experimentally and mathematically unquestionable phenomenological treatments based on the perfect conductor premise. With the foregoing in mind it is understandable how the entire scientific world was kept within the bounds of its own preconceived myth (save for a visionary few).
In the intervening years between the discovery of the Meissner Effect and the introduction of the microscopic theory in 1957, investigators sought after two rather elusive points: (A) A theory which would explain the perfect electrical conduction and Meissner Effect coupled with experimentally found limits underwhich superconductivity may occur: below a certain maximum applied magnetic field and under a particular highest ambient temperature, and (B) superconductive materials which would retin their unique properties in very high fields and temperatures.
During this period some confusion resulted because of lack of universal recognition for many years of two classes of superconductors and the distinction between various phases within each class. Eventually, experimentation proved that: (A) Type I superconductors of the soft metals had a low critical field and temperature and entered an intermediate state of alternate domains of superconductive and normal material when the geometry of the sample was other than a thin cylinder in a longitudinal mgnetic field and the applied field reached a locally critical intensity, and (B) Type II superconductors of the hard metals and alloys had comparatively high critical field and temperatures and entered a mixed phase state above a certain less than critical magnetic field independent of sample geometry. The intermediate state and mixed phase state were often confused and generally research was somewhat minimal since practical use of this phenomenon looked very far away indeed due to temperature (maximum round 7.2.degree. K. for Pb) and field (maximum around 803 gauss for Pb) limitations.
The greater part of scientific research has actually been done since Yntema in 1955 created the first successful high field superconductive electromagnet by using unannealed niobium wire to attain 7.1 Kgauss. He was soon followed by other experimenters who made use of cold working technology to improve the performance of niobium windings. Finally, since 1961 Kunzler and others successfully developed alloying techniques which produced Type II superconductors capable of withstanding (NbSn: 200 Kgauss & 18.degree. K.) inordinately high fields and almost "warm" temperatures, before losing their superconductive properties. This ushered in a new era of applied research and development, including: computer switching elements, motors, generators, magnets, and lossless bearings, nearly lossless power transmission lines and transformers, etc.
The Bardeen Cooper Schrieffer Theory of 1957 explained the phenomenological theories of F. London on a microscopic basis. Superconductivity was understood to be: (A) a condensation to lower energy by so-called superelectrons due to a quantum mechanical electron pairing process, (B) this pairing process was seen to occur only within a finite distance, the Coherence Length, which, if longer or shorter than the depth to which a field penetrates into the surface of a sample, meant it was either Type I or Type II, respectively, (C) the critical fields and temperatures were then just the necessary energy inputs to raise the superelectrons of zero resistance to normal electrons of finite resistance, that is, the electron "fluids" were separated by an energy-gap, and (D) the Meissner Effect was due to a sudden condensation energy outflux at the transition, an energy capable of doing magnetic work.
More recently, research is pressing forward at an ever accelerating pace to achieve room temperature superconductors. Some feel that this may be possible by using the long and essentially one dimensional organic molecule, which possesses the necessary symmetry requirements. Some success has been reported, with the present high at approximately 24.degree. K. Generators, motors, power lines and rail transport levitation schemes, using superconductors, have been constructed and successfully tested.
The Invention is a process cycle for a heat engine utilizing superconductors in the temperature range near absolute zero, in which an applied magnetic field may alternatively be present within, or expelled from, the interior of the subject superconductor, the net effect being to do work on the field, which may then be tapped as a net useful work output. The source of such work to eject the magnetic flux emanates from the quantum mechanical condensation energy responsible for the superconductive state. Any magnetic work performed is accomplished by use of the superconductor's internal energy, resulting in a net latent heat of cooling, for which a heat influx from an external hot temperature heat reservoir is required to complete the cycle. The said cycle involves the adiabatic magneto-caloric effect, with an imposed limiting size constraint on the superconductive particles which will not admit the presence of an intermediate state during phase transition.
A superconductor at or near zero degrees Kelvin can expel an applied internal magnetic field by simply lowering the field below a critical value. This "Meissner Effect" result does work on the applied field, the energy for which comes from the internal energy of the superconductor. The phase transition process is one resulting from a quantum mechanical condensation in the conduction electrons. It will be seen in the following Description of the Invention (particularly graphical FIGS. 3 through 18, together with the relevant description pertaining thereto) that the essence of the cycle ability to convert ambient heat into work derives from quantum mechanical, not thermal, sources. That is, in any process herein discussed all thermally associated thermodynamic process paths are reversible--there is no ambient heat conversions into work resulting therefrom (as is usually the case with the quantum mechanical portion of the energies contribution in the macroscopic size magneto-caloric effect). However, as will be more fully described below, a singular means is provided in accordance with the present invention (substantially, when the size of the superconductor is less than the range of coherence and at least five times the field penetration depth) to cause the quantum mechanical energies of the superconductive phase to have a macroscopic effect and contribute, in a directed manner, to the thermal processes, resulting in an irreversible process of phase transition, the net effect of which converting ambient heat into useful work, in consistency with the Second Law of Thermodynamics.
The process cycle, in accordance with the present invention, may be adapted for either motor or generator type energies output. In the case of the motor, an energy density of substantially fifty horse power per cubic foot will permit use in mobile as well as stationary employments, i.e., transportation, aviation, nautical and agricultural, as well as household and industrial mechanisms. In the case of the generator, both large utilities and individual consumers may benefit. Uses may range from electrical generating facilities to units no larger than flashlight batteries.
Because no waste heat generates, no low temperature reservoir is needed, nor must energy be invested for its removal. Consequently, any suitable ambient heat source will serve as fuel, which opens a vast use potential hinged on ease of access and availability of motive fuel. For example, the atmosphere is a good heat source, as is the ocean.
As a benefit from operation at cryogenic temperatures, magnetic flux confinement shields of superconductive sheet can be used to minimize and homogenize the magnetic circuit. Further, use of superconductive magnetic bearings offer significant operational efficiencies and life-times.
The type of superconductors suitable for utilization are of the elemental (Type I) kind, i.e., tin, aluminum, indium, and mercury. These are readily available, and easily purified and machined. Much current cyrogenic technology may be immediately adapted. The self-cooling nature of certain cyclical options obviates the need for refrigeration or cryogenic gases.
The cycle offers exceptional attractiveness for utilization in a vast range of present mechanisms in which work must be produced or heat must be moved.